my centroid for x = (75x175)(37.5) +(100x175) (125) + (0.5x50x175)(225)-(π/4 x100x100)(175 - (4(100)/3π) ) / 27964 = 37.26 , but the ans given is x = 102 , y= 62.5 , which part of my working is wrong ?
p/s : i have divided the areas into 4 parts , the first is the (75x175) reactangle , second is (100x175) trianlgle , fourth is -(π/4 x100x100) , the third is the triangle (0.5x50x175)

For some reason, you are showing the wrong dimensions of the end triangle here in calculating the moment. The triangle should be L = 150 mm, H = 75 mm
Also, you are dividing by the incorrect area calculated in step one.

You're still not checking your work to eliminate silly mistakes, like using the incorrect dimensions of the end triangle.

Please re-do your calculations.

P.S.: I found a mistake in my own calculations. My calculations for the centroid location now agree with the values shown for x-bar and y-bar in the image attached to the OP.